The actor told IndieWire that he didn't quite know what he was getting himself into with the Zellner brothers' oddball western, but that's sort of his thing these days.

When Robert Pattinson first received the script for the David and Nathan Zellners’ “Damsel,” a quirky, inverted western in which various cockeyed suitors pine for love of a woman disinterested in their advances, he passed. “It just seemed like one of those things that’s never going to get financing, so it just didn’t really register with me,” he said.

A few weeks later, he went to see “Kumiko, the Treasure Hunter” in theaters, not realizing it came from the same sibling director pair. He called his agent, eager to meet whoever was behind it.

“He was like, yeah, you just got offered a role for their new movie and you didn’t meet with them,” Pattinson recalled. He circled back on “Damsel,” which sees him entering strange terrain for an actor whose penchant for stone-faced roles has evolved from the “Twilight” franchise to auteur-driven work like David Cronenberg’s “Cosmopolis” and the Safdie brothers’ “Good Time.” As Samuel Alabaster, the foolishly overconfident pioneer eager to rescue Penelope (Mia Wasichowska) from her supposed captors even though she may not want the help, Pattinson found himself in the unlikely position of a comedic role.

That was something he didn’t expect when he signed up, in part because the melancholic “Kumiko” — in which a Japanese woman, believing the plot of “Fargo” to be real, gets lost in Nebraska — had a totally different feel. “‘Kumiko’ is one of the strangest movies ever,” Pattinson said. “To have such an odd movie and make it coherent and kind of touching, the aesthetic of it is really elegant of it, and kind of cool, too — they had a lot going on at the same time. Connecting that with the script for ‘Damsel’ felt really left field to me.”

When he read “Damsel,” he said, “it didn’t read necessarily as a straight comedy, it just felt really odd.” Still trying to figure how to classify the movie after production wrapped, he dug back into the Zellners’ filmography and watched “Kid-Thing,” their dark, lyrical story of a young girl who hears a voice down the well. Unlike “Kumiko,” the Zellners’ first project on a bigger budget, “Kid-Thing” conveys their off-beat, deadpan humor in clearer terms. He recognized that while “Kumiko” had a “stately” feel to it, the Austin-based filmmakers’ other movies were “more ramshackle.”

Still, “Damsel” doesn’t signal some new phase of Pattinson’s career in studio rom-coms. While Samuel commands the first act of the movie, his obsession with finding the girl of his dreams required the actor play it straight. “The guy is completely psychotic,” Pattinson said. “He’s never done anything more nefarious than annoying people, but his capacity for delusion is kind of frightening. He’s not a bumbling moron. His actions are very premeditated. He’s deeply, deeply mad. I was approaching it like that.”

In one standout moment from the movie, Samuel performs an entire song on acoustic guitar that he’s written for Penelope. Searching for a way to categorize the movie he was making, he hoped to make the crew laugh. “There were scenes where nobody was laughing,” he said. “I was trying to get a reaction from people. With that song, I finally saw the boom operator smiling, and it was the biggest relief.”

He admitted to feeling unsure about how the project could possibly gel in completed form. The story finds Samuel and a bumbling preacher named Parson (David Zellner) stumbling through the wilderness until they come across Penelope, and then the context of the movie shifts in a completely unexpected direction. “Halfway through the shoot, I’d completely lost the plot and had no idea what was going on,” he said. The Sundance premiere brought him someone measure of relief. “I’m always surprised when something makes sense,” he said. “It turns out someone was in control.”

“Damsel” evolves from a deconstruction of masculine westerns into a feminist-leaning narrative that has additional potency in the #MeToo era, even though the movement emerged long after the movie had wrapped.

”I always found it interesting that it’s turning an unrequited love story on its head,” Pattinson said. “It’s normally presented as a pretty tragic thing. But if you are the object of unrequited love, it’s actually really irritating, especially when the person just refuses to stop. I think men and women are both guilty of it.”

Nevertheless, the actor said he wasn’t using any barometer for representation or political correctness when choosing his projects. “I don’t like archetypes in movies,” he said. “I think they’re boring.” He’s tired of seeing “a stream of typical storytelling with the male gaze,” but cautioned against “just having a bunch of these movies where they swap the male character with a female character.”

He explained: “I don’t really know what the point of that would be. I always look for scripts where all the characters are multifaceted and original. I’m looking for something new more than anything else. I don’t want to find something that just reinforces my worldview.”

His career post-“Twilight” backs up that assessment. Over the past six years he has surfaced in a range of unorthodox projects, none of which have much in common: two Cronenberg movies, David Michod’s unorthodox post-apocalyptic western “The Rover,” Werner Herzog’s “Queen of the Desert,” Brady Corbet’s “The Childhood of a Leader,” James Grey’s swashbuckling jungle adventure “The Lost City of Z,” and the Safdies’ “Good Time.” He’s played wanderers, simpletons, criminals, and playboys. And the 32-year-old is just getting started.

Robert Pattinson

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Later this year, he’ll appear in Claire Denis’ “High Life,” an arty space odyssey that marks the veteran French director’s most ambitious project and her first venture into the sci-fi realm. “I saw a rough cut the other day and I think it’s great, so bizarre,” he said. “I’m very curious how people will see it.”

He also just finished production on “The Lighthouse,” Robert Eggers’ followup to his New England horror tale “The Witch.” Shot on black-and-white 16mm in Nova Scotia to stand in for Maine, the story revolves around an early 20th century lighthouse where strange events transpire. “It was really hard,” Pattinson said. “I’d never spent so much time under rain in my life, in scene after scene after scene, just soaking wet after two months.” He felt vindicated by some of the early processed footage he saw. “I think it’s going to be pretty crazy,” he said. “I’ve only seen a couple of moments from it, but it looks like a Buster Keaton movie.”

In a few weeks he’s off to the U.K., reuniting with David Michod for his latest production. Then there are the projects in the pipeline that he hopes will come together. These include Olivier Assayas’ “Idol’s Eye,” a sprawling crime drama said to co-star Sylvester Stallone, but the project has been reported on for over two years.

“Every six months or so, it seems like it’ll reappear,” he said. “I saw Olivier talking about it the other day. It’s just one of those things that’s kind of expensive. But it’s a great script — a real epic, like 180 pages long.”

He’s hoping to work with rising U.K. director Joanna Hogg on the second half of her two-part film odyssey “The Souvenir,” after the first half surfaces later this year. “That’s a very, very ambitious project,” Pattinson said. “I’m hoping to see the first part in a couple of weeks.”

And he wants to work with his friend Antonio Campos, part of the Borderline Films collective, for the first time on “The Devil All the Time.” He said the project, a post-war drama that spans several decades, called for him to play “another psychopathic character.” He giggled. “I seem to enjoy playing those,” he said.